34 EOKABT [chap. 2 



v' and v" being the two coefficients of viscosity. The heat generated by viscosity 

 is then 



+ K-§v')(V.u)2 (15) 



and will be positive provided that 3v" > 2v' > 0. 

 Fourier's law of heat conduction is 



h = -kVB, (16) 



and hence the heat generated by the irreversible conduction of heat is 



-h-V0 = /c(V^)2 (17) 



and will be positive if /c> 0. 



Accepting the Stokes-Navier and Fourier laws, the simplest law of diffusion 

 consistent with the uniform positiveness of is 



s = -DVjM (18) 



where D>0. Fick's law of diffusion (see (20), below) is not consistent with this 

 requirement, but is an approximation to (18) under certain conditions. This 

 will now be proven. 



Equation (1) expresses the potential /a, as a function of v, 17 and S; it can 

 also be expressed in terms of ^, ^ and S. Then (18) may be written 



Now, in the laboratory experiments that confirm Fick's law, conditions are 

 controlled so that the pressure and temperature gradients are of no importance, 

 while the effects of salinity gradients are maximized. Under these conditions 



s = -DsVS (20) 



where Ds = D{diildS) is Fick's coefficient of diffusion. 



In the laboratory it is easy to modify the experimental conditions so that 

 thermal diffusion occurs ; in extreme cases, the effect of the temperature 

 gradient dominates those of pressure and salinity, and then 



s = -DrV0 (21) 



where Dt = D{dfxldd) is the coefficient of thermal diffusion. Finally, in centri- 

 fuge experiments (usually conducted only with solutes of high molecular 

 weight but in principle applicable to any solute) the effect of the pressure 

 gradient dominates, and 



s = -DpVp (22) 



where Dp= D{dfjLl8p). 



